The Beauty of Mathematics in Computer Science: 1st Edition (Paperback) book cover

The Beauty of Mathematics in Computer Science

1st Edition

By Jun Wu

Chapman and Hall/CRC

268 pages

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Paperback: 9781138049604
pub: 2018-11-05
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Description

The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school.

The book covers many topics related to computer applications and applied mathematics including: Natural language processing

Speech recognition and machine translation

Statistical language modeling

Quantitive measurement of information

Graph theory and web crawler

Pagerank for web search

Matrix operation and document classification

Mathematical background of big data

Neural networks and Google’s deep learning

Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

Table of Contents

1. Words and languages, numbers and information

Information

Words and numbers

The mathematics behind language

2. Natural language processing|From rules to statistics

Machine intelligence

From rules to statistics

3. Statistical language model

Describing language through mathematics

Extended reading: Implementation caveats

Higher order language models

Training methods, zero-probability problems, and smoothing

Corpus selection

4. Word segmentation

Evolution of Chinese word segmentation

Extended reading: evaluating results

Consistency

Granularity

5. Hidden Markov model

Communication models

Hidden Markov model

Extended reading: HMM training

6. Quantifying information

Information entropy

Role of information

Mutual information

Extended reading: Relative entropy

7. Jelinek and modern language processing

Early life

From Watergate to Monica Lewinsky

An old man's miracle

8. Boolean algebra and search engines

Boolean algebra

Indexing

9. Graph theory and web crawlers

Graph theory

Web crawlers

Extended reading: two topics in graph theory

Euler's proof of the Königsberg bridges

The engineering of a web crawler

10.PageRank: Google's democratic ranking technology

The PageRank algorithm

Extended reading: PageRank calculations

11.Relevance in web search

TF-IDF

Extended reading: TF-IDF and information theory

12.Finite state machines and dynamic programming: Navigation in Google Maps

Address analysis and Finite state machines

Global navigation and dynamic programming

Finite state transducer

13.Google's AK- designer, Dr Amit Singhal

14.Cosines and news classification

Feature vectors for news

Vector distance

Extended reading: The art of computing cosines

Cosines in big data

Positional weighting

15.Solving classification problems in text processing with matrices

Matrices of words and texts

Extended reading: Singular value decomposition method and applications

16.Information Fingerprinting and its application

Information Fingerprint

Applications of information Fingerprint

Determining identical sets

Detecting similar sets

YouTube's anti-piracy

Extended reading: Information Fingerprint's repeatability and SimHash

Probability of repeated information Fingerprint

SimHash

17.Thoughts inspired by the Chinese TV series Plot: The mathematical principles of cryptography

The spontaneous era of cryptography

Cryptography in the information age

18.Not all that glitters is gold: Search engine's anti-SPAM problem and search result authoritativeness question

Search engine anti-SPAM

Authoritativeness of search results

Summary

19.Discussion on the importance of mathematical models

20.Don't put all your eggs in one basket: The principle of maximum entropy

Principle of maximum entropy and maximum entropy model

Extended reading: Maximum entropy model training

21.Mathematical principles of pinyin input method

Input method and coding

How many keystrokes to type a Chinese character?

Discussion on Shannon's First Theorem

The algorithm of phonetic transcription

Extended reading: Personalized language models

22.Bloom Filters

The principle of Bloom Filters

Extended reading: The false alarm problem of Bloom Filters

23.Bayesian network: Extension of Markov Chain

Bayesian network

Bayesian network's application in word classification

Extended reading: Training a Bayesian network

24.Conditional random Fields, syntactic parsing, and more

Syntactic parsing|the evolution of computer algorithms

Conditional random fields

Conditional random fields' applications in other fields

25.Andrew Viterbi and the Viterbi Algorithm

The Viterbi algorithm

CDMA technology: The foundation of G mobile communication

26.God's algorithm: The expectation maximization algorithm

Self-converged document classification

Extended reading: Convergence of expectation-maximization algorithms

27.Logistic regression and web search advertisement

The evaluation of web search advertisement

The logistic model

28.Google Brain and artificial neural networks

Artificial neural network

Training an artificial neural network

The relationship between artificial neural networks and

Bayesian networks

Extended reading: \Google Brain"

29.The power of big data

The importance of data

Statistics and information technology

Why we need big data

About the Author

Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese internet users from 2006-2010. The blogs had more than two million followers. He received Ph.D. in computer science from the Johns Hopkins University and had been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded more than ten US patents during his ten-year tenure there. He became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

Subject Categories

BISAC Subject Codes/Headings:
BUS061000
BUSINESS & ECONOMICS / Statistics
COM037000
COMPUTERS / Machine Theory
COM083000
COMPUTERS / Security / Cryptography